In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-L...In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vincity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a 'sharp' condition on limiter function in order to keep its entropy dissipation and its convergence.展开更多
A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expre...A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expression and is easy for use in CFD codes.Compared with the original second-order or third-order MUSCL scheme,the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves.This new scheme has been tested through a set of one-dimensional and two-dimensional tests,including the Shu-Osher problem,the Sod problem,the Lax problem,the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test.All numerical tests show that,compared with the original MUSCL schemes,the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.展开更多
This is the continuation of the paper”Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction”by the same authors.The hierarchical reconstruction introduced the...This is the continuation of the paper”Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction”by the same authors.The hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to finite volume schemes on non-staggered grids.This takes a new finite volume approach for approximating non-smooth solutions.A critical step for high-order finite volume schemes is to reconstruct a non-oscillatory high degree polynomial approximation in each cell out of nearby cell averages.In the paper this procedure is accomplished in two steps:first to reconstruct a high degree polynomial in each cell by using e.g.,a central reconstruction,which is easy to do despite the fact that the reconstructed polynomial could be oscillatory;then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high resolution.All numerical computations for systems of conservation laws are performed without characteristic decomposition.In particular,we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th-order schemes without characteristic decomposition.展开更多
文摘In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vincity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a 'sharp' condition on limiter function in order to keep its entropy dissipation and its convergence.
基金supported by the National Natural Science Foundation of China (Grant Nos.10632050,10872205,11072248)the National Basic Research Program of China (Grant No.2009CB724100)+1 种基金the National High Technology Research and Development Program of China (Grant No.2009AA010A139)the Chinese Academy Sciences Program (Grant No.KJCX 2-EW-J01)
文摘A second-order optimized monotonicity-preserving MUSCL scheme(OMUSCL2) is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique.The new scheme(OMUSCL2) is simple in expression and is easy for use in CFD codes.Compared with the original second-order or third-order MUSCL scheme,the new scheme shows nearly the same CPU cost and higher resolution to shockwaves and small-scale waves.This new scheme has been tested through a set of one-dimensional and two-dimensional tests,including the Shu-Osher problem,the Sod problem,the Lax problem,the two-dimensional double Mach reflection and the RAE2822 transonic airfoil test.All numerical tests show that,compared with the original MUSCL schemes,the new scheme causes fewer dispersion and dissipation errors and produces higher resolution.
基金supported in part by NSF grant DMS-0511815.The research of C.-W.Shu was supported in part by the Chinese Academy of Sciences while this author was visiting the University of Science and Technology of China(grant 2004-1-8)+3 种基金the Institute of Computational Mathematics and Scientific/Engineering ComputingAdditional support was provided by ARO grant W911NF-04-1-0291 and NSF grant DMS0510345The research of E.Tadmor was supported in part by NSF grant 04-07704 and ONR grant N00014-91-J-1076The research of M.Zhang was supported in part by the Chinese Academy of Sciences grant 2004-1-8.
文摘This is the continuation of the paper”Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction”by the same authors.The hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to finite volume schemes on non-staggered grids.This takes a new finite volume approach for approximating non-smooth solutions.A critical step for high-order finite volume schemes is to reconstruct a non-oscillatory high degree polynomial approximation in each cell out of nearby cell averages.In the paper this procedure is accomplished in two steps:first to reconstruct a high degree polynomial in each cell by using e.g.,a central reconstruction,which is easy to do despite the fact that the reconstructed polynomial could be oscillatory;then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high resolution.All numerical computations for systems of conservation laws are performed without characteristic decomposition.In particular,we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th-order schemes without characteristic decomposition.
